Results of Hankel Semigroup of Linear Operator as Eventually Uniform Continuous Semigroup

This paper consists of Hankel results of ω-order reversing partial contraction as a semigroup of linear operator. Spectral mapping theorem was investigated and it was established that ω-order reversing partial contraction mapping is an eventually uniform continuous semigroup in which we showed that the proof of the extension of T (t) to a C₀-semigroup ̂T(t) on a space ̂X containing X isometrically bounded. The space is constructed in such a way that the spectrum of the generator A of T (t) coincides with the spectrum of the generator  of ̂T(t) and the approximate point spectrum of A coincides with the point spectrum of Â.